The long-term objective of this research is to achieve in medical ultrasonic imaging diffraction-limited focus characteristics and corresponding high image quality through inhomogeneous tissue (such as abdominal wall, chest wall, and the female breast). The specific aims are to evaluate adaptive imaging algorithms that have been proposed and to develop new algorithms by constructing models of the wavefront distortion. The method is to estimate and compensate for propagation inhomogeneities that lie between the array and the region of interest. The investigation will employ a synergistic combination of simulations and experiments. The simulations will accurately model the array, propagation inhomogeneities, and the scattering process. An adaptation of the k-space method will be used for computation of wavepropagation through an inhomogeneous medium. The experiments will use an 8Ox8O- element 3.0-MHz two-dimensional array with programmable transmit waveforms. This apparatus enables the implementation of adaptive imaging algorithms that perform not only time-shift compensation but also waveform shape compensation on transmit. The transmit beam size effect on time-delay estimation and the isoplanatic patch size of the compensation algorithms will be quantified. Phantoms that mimic the distortion effects of human tissue will be constructed. Implementation of the algorithms with a sparse 2-D array and with a 1-D array will also be studied. The algorithms will be evaluated in terms of point and contrast resolution, computational complexity, isoplanatic patch size, and number of transmit iterations required for the convergence of distortion estimation. New algorithms for adaptive ultrasonic imaging will be developed based on wavefront propagation and processing. The simulations and experiments will complement and strengthen each other in the investigation of various imaging conditions and in providing physical verification of the effectiveness of adaptive imaging. Through this research, ultrasonic imaging in the presence of propagation inhomogeneities will be achieved with the highest possible resolution and the utility of ultrasound in the early and accurate diagnosis of diseases such as the breast cancer will be greatly expanded.